L1 analysis of sampled-data systems via fast-lifting and piecewise linear approximation

This paper revisits the L₁ analysis of sampled-data systems, by which we mean the computation of the L_∞-induced norm of sampled-data systems. More precisely, we apply fast-lifting by which the sampling interval [0, h) is divided into M subintervals with an equal width, and provide a method for computing the L_∞-induced norm by using an idea of piecewise linear approximation. Through this method, we show that we can compute upper bound and lower bounds of the L_∞-induced norm and that the computation error associated with this method converges to 0 at the rate of 1/M². This is in sharp contrast with a conventional method via fast-sample/fast-hold approximation, which only shows that the computation error converges to 0 in the rate of 1/M, without providing any explicit upper and lower bounds of the L_∞-induced norm.